Environmental

Statistics

Statistics, down to Earth

Course Outline

Our flagship course, taught over 4.5 days.

DAY 1

Describing Data

When to tuse a median vs a mean

Dealing with skewed, non-normal data

Dealing with outliers

When to transform the scale

Seven Urban Legends in Environmental Statistics

Do parametric methods have more power than nonparametric tests?

Why t-tests on logarithms don't test differences in means

Why t-tests don't test whether one group has higher values than the second

and more....

How Hypothesis Tests Work

Structure of hypothesis testing

Their jargon explained

Parametric, nonparametric and permutation tests. When to use each.

1-sided and 2-sided tests

Checking data distributions

Illustration: How tests obtain a p-value

Statistical Intervals

Confidence, prediction, tolerance intervals

Intervals with small sample sizes

Coping with skewed data

Bootstrap intervals — and why to use them instead of t-intervals

Exercise: the UCL95 and other intervals

DAY 2

Comparing Two Groups of Data

Are means, medians different?

Parametric, nonparametric and permutation tests

Testing paired data

Have standards been met?

The quantile test

Permutation tests — test the mean for non-normal distributions*(if there’s time)* How many observations do I need?

Power and sample size

Which units to use?

Numbers of obs for parametric and non-parametric tests

Software available

Comparing Three or More Groups

One- and two-factor ANOVA

Nonparametric Kruskal-Wallis test

Multiple comparison tests: who’s different?

Permutation one-factor test: never worry about a normal distribution again!

Testing differences in Variability/Precision

Characterizing differences in variability

Levene’s & Fligner-Killeen tests

Why NOT to use Bartlett’s test

DAY 3

Correlation

Linear and monotonic correlation

r, rho and tau

Permutation test for Pearson’s r correlation

The Theil-Sen line: a linear median

Linear Regression

Building a good regression model

Better measures of quality than r-squared

Hypothesis tests, confidence and prediction intervals

Consequences of transforming the Y variable

Bootstrapping tests for significance - an alternative to transformations

Multiple Regression

How to build a good multiple regression model

Why plots of Y vs each X don't work, and what to do instead

Multi-collinearity

Model selection methods better than r-squared or stepwise

Bootstrapping tests for significance - an alternative to transformations

DAY 4

Analysis of Covariance

Testing whether there is one or more than one regression line

Are there differences in intercept and slope?

Modeling seasonal changes

Trend Analysis

Selecting a trend test

Regression vs. Mann-Kendall approaches

Monotonic vs. step trends

Dealing with seasonality: the Seasonal-Kendall test for trend

Detecting consistent regional trends across sites

R routines for trend testing

FINAL EXAM

DAY 5 (half day)

Handling Nondetect Data Correctly

Why not substitute 1/2 the detection limit?

Simple methods without substitution

Introduction to survival analysis methods

Contingency Tables

Does the frequency change between groups?

Application to nondetect and other cateogories

Bootstrapping contingency tables

Logistic Regression

Regression for categorical responses

Effect of X variables on the odds

Modeling nondetects, qualitative methods, and the probability of something bad happening

Multicollinearity and hypothesis tests